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Accelerated Diagonal Steepest Descent Method for Unconstrained Multiobjective Optimization

Author

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  • Mustapha El Moudden

    (Mohammed VI Polytechnic University)

  • Abdelkrim El Mouatasim

    (Ibn Zohr University)

Abstract

In this paper, we propose two methods for solving unconstrained multiobjective optimization problems. First, we present a diagonal steepest descent method, in which, at each iteration, a common diagonal matrix is used to approximate the Hessian of every objective function. This method works directly with the objective functions, without using any kind of a priori chosen parameters. It is proved that accumulation points of the sequence generated by the method are Pareto-critical points under standard assumptions. Based on this approach and on the Nesterov step strategy, an improved version of the method is proposed and its convergence rate is analyzed. Finally, computational experiments are presented in order to analyze the performance of the proposed methods.

Suggested Citation

  • Mustapha El Moudden & Abdelkrim El Mouatasim, 2021. "Accelerated Diagonal Steepest Descent Method for Unconstrained Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 188(1), pages 220-242, January.
    • Handle: RePEc:spr:joptap:v:188:y:2021:i:1:d:10.1007_s10957-020-01785-9
    DOI: 10.1007/s10957-020-01785-9
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    References listed on IDEAS

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    1. Markus Hartikainen & Kaisa Miettinen & Margaret Wiecek, 2012. "PAINT: Pareto front interpolation for nonlinear multiobjective optimization," Computational Optimization and Applications, Springer, vol. 52(3), pages 845-867, July.
    2. Jörg Fliege & Benar Fux Svaiter, 2000. "Steepest descent methods for multicriteria optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(3), pages 479-494, August.
    3. Prabuddha De & Jay B. Ghosh & Charles E. Wells, 1992. "On the Minimization of Completion Time Variance with a Bicriteria Extension," Operations Research, INFORMS, vol. 40(6), pages 1148-1155, December.
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    Cited by:

    1. Hiroki Tanabe & Ellen H. Fukuda & Nobuo Yamashita, 2023. "An accelerated proximal gradient method for multiobjective optimization," Computational Optimization and Applications, Springer, vol. 86(2), pages 421-455, November.
    2. Qing-Rui He & Sheng-Jie Li & Bo-Ya Zhang & Chun-Rong Chen, 2024. "A family of conjugate gradient methods with guaranteed positiveness and descent for vector optimization," Computational Optimization and Applications, Springer, vol. 89(3), pages 805-842, December.
    3. Qing-Rui He & Chun-Rong Chen & Sheng-Jie Li, 2023. "Spectral conjugate gradient methods for vector optimization problems," Computational Optimization and Applications, Springer, vol. 86(2), pages 457-489, November.

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